Plotting absolute stability regions

$$\pi(\xi;z) = \rho(\xi) - z \sigma(\xi) = 0$$

For each value of $z$, this polynomial has some number of roots that, of course, change as $z$ varies.

Recall that the "possible boundary" of the stability region $S$ is given by

$$ \frac{\rho(e^{i \theta})}{\sigma(e^{i\theta})}, \quad \theta \in [0,2 \pi). $$

Find the roots of

\begin{align*} \zeta^2 - \zeta = 0 \end{align*}